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A Model of Random Matching

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  • Itzhak Gilboa
  • Akihiko Matsui

Abstract

This paper presents a model of random matching between individuals chosen from large populations. We assume that the populations and the set of encounters are infinite but countable and that the encounters are i.i.d. random variables. Furthermore, the probability distribution on individuals according to which they are chosen for each encounter is "uniform", which also implies that it is only finitely additive. Although the probability measure which governs the whole matching process also fails to be (fully) sigma-additive, it still retains enough continuity properties to allow for the use of the law of large numbers. This, in turn, guarantees that the aggregate process will (almost surely) behave "nicely", i.e., that there will be no aggregate uncertainty.

Suggested Citation

  • Itzhak Gilboa & Akihiko Matsui, 1990. "A Model of Random Matching," Discussion Papers 887, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:887
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    1. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    2. Weiss, Ernst-August Jr., 1981. "Finitely additive exchange economies," Journal of Mathematical Economics, Elsevier, vol. 8(3), pages 221-240, October.
    3. Armstrong, Thomas E. & Richter, Marcel K., 1984. "The core-walras equivalence," Journal of Economic Theory, Elsevier, vol. 33(1), pages 116-151, June.
    4. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-1169, September.
    5. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    6. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
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